Related papers: A unifying framework for perturbative exponential …
We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
From a transfer formula in multivariate finite operator calculus, comes an expansion for the determinant similar to Ryser's formula for the permanent. Although this one contains many more terms than the usual determinant formula. To prove…
A variational framework is developed here to quantize fermionic fields based on the extended stationary action principle. From the first principle, we successfully derive the well-known Floreanini-Jackiw representation of the…
We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic…
In this paper, we establish the decomposition of morphisms from lattice of subgroup sets to generalized solvable extension formations. To achieve this, we develop a unified framework involving maximal subgroup functors, generating formation…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
We present an upgraded formula for Wigner function and spin polarization of fermions emitted by a relativistic fluid at local thermodynamic equilibrium at the decoupling which improves the one obtained in refs. [1, 2] and used in numerical…
The systematic expansion method of the solution of the Fokker-Planck equation is developed by generalizing the formulation proposed in [J. Phys. A50, 325001 (2017)]. Using this method, we obtain a new formula to calculate the mean work…
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…
Estimating causal effects from observational data (at either an individual -- or a population -- level) is critical for making many types of decisions. One approach to address this task is to learn decomposed representations of the…
We describe discretisations of the shallow water equations on the sphere using the framework of finite element exterior calculus, which are extensions of the mimetic finite difference framework presented in Ringler, Thuburn, Klemp, and…
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…
A Cumulant based method has been introduced to extract quantum corrections in distribution function with the equilibrium Wigner-Boltzmann equation. It is shown that unlike the moment expansion used in hydrodynamic model, cumulant expansion…
The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…
Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We…
We propose a causal predictive framework for estimating risk under preventative interventions. The Unexposed Mediator Model maintains mediators that are also predictors at their unexposed level, removing double counting of intervention…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…